1

1
The Level and Quality of Value-at-Risk Disclosure
by Commercial Banks Christophe Pérignon HEC
Paris Daniel R. Smith Simon Fraser
University Risk Management in Financial
Institutions 23-25 April 2009
2

• Introduction
• Disclosure of quantitative measures of market
  risk such as value-at-risk is enlightening only
  when accompanied by a thorough discussion of how
  the risk measures were calculated and how they
  related to actual performance
• Alan Greenspan

3
VaR is a quantile of the trading revenue (PL)
distribution
e.g. Bank of America VaR(99 1 day) on December
31 2008 was 140 mio
1-day ahead P/L distribution
Losses
Gains
VaR(99 1 day)
4
VaR is a quantile of the trading revenue (PL)
distribution
Increase in Volatility
Losses
Gains
VaR
VaR
5

• Our Objective
• Joint Assessment of
• Level Quality
• of VaR disclosure by commercial banks
• When quantity and quality are both at acceptable
  levels Reduction in information asymmetry

6

• Our Contributions
• Survey of actual VaR disclosures in the world
• Formal test of whether daily VaRs are
• Accurate Lead to the correct number of
  exceptions
• Informative Forecast next-day volatility of
  trading revenues

7

• Part 1 Level of VaR Disclosure
• VaR Disclosure Index (VaRDI)
• Sample 10 largest US commercial banks 6 largest
  Canadian commercial banks and top-50
  international commercial banks
• Sample Period Entire post-1996 Market Risk
  Amendment period for US and Canadian banks and
  year 2005 for top-50 international banks
• Data Source Annual reports

8

• VaR Disclosure Index (VaRDI)
• 1. VaR Characteristics
• a. Score of 1 if Holding Period (e.g. 1 day
  1 month)
• b. Score of 1 if Confidence Level (e.g. 99
  95)
• 2. Summary VaR Statistics
• a. Score of 1 if High Low or Average VaR
• b. Score of 1 if Year-End VaR
• c. Score of 1 if VaR by Risk Category (e.g.
  Currency Fixed Income Equity)
• d. Score of 1 if Diversification Effect is
  accounted for
• 3. Intertemporal Comparison
• a. Score of 1 if Summary Information about
  the Previous Year VaR
• 4. Daily VaR Figures
• a. Score of 1 if Histogram of Daily VaRs or
  score of 2 if Plot of Daily VaRs
• 5. Trading Revenues
• a. Score of 1 if Hypothetical Revenues
• b. Score of 1 if Revenues without Trading
  Fees
• c. Score of 1 if Histogram of Daily
  Revenues or score of 2 if Plot of Daily
• Revenues

9

• VaRDI for 10 Largest US Banks (1/2)

10

• VaRDI for 10 Largest US Banks (2/2)

11

• VaRDI in the U.S. and in Canada (1996-2005)

12

• VaRDI in the World (2005)

13

• VaRDI by Country (2005)

14

• VaR Methods Currently Used by Banks (2005)

15

• Historical Simulation (HS)
• HS method based on the one-year unconditional
  distribution of the risk factors
• HS-based VaRs are under-responsive to changes in
  conditional risk
• Mechanical disconnection between 1-day VaR and
  actual volatility on the next day
• True in practice

16

• Part 2 Quality of VaR Disclosure
• Backtesting
• Forecast Trading Revenue Volatility

17

• Part 2a Backtesting

18

• Part 2b Forecasting Trading Revenue Volatility
• For each country included in our survey we look
  for a bank disclosing a graph of daily VaR and
  trading revenues over a long enough sample period
• Bank of America (US)
• Credit Suisse First Boston (Switzerland)
• Deutsche Bank (Germany)
• Royal Bank of Canada (Canada)
• Société Générale (France)
• All banks have VaRDIs of at least 13 points
• They all use Historical Simulation except
  Deutsche Bank

19

• Data Extraction
• Actual VaRs and trading revenues are not
  available in a machine-readable format
• We extract the data from the graphs included in
  annual reports using a Matlab-based technique
• Convert PDF file into JPG
• Import JPG file into Matlab
• Add vertical lines on the image
• Zoom in and click on each data point
• Convert Matlab coordinates into graph coordinates
• Many experiments and simulations are presented in
  the appendix

20
Bank of America Credit Suisse First
Boston Deutsche Bank Royal Bank of
Canada Societé Générale
The Bank of America
21

• Measuring VaR Accuracy
• We look for a statistical link between VaRt1t
  and the volatility of the trading revenue Rt1
• We use a simple GARCH model as a benchmark
• Unfair horse race risk manager knows the
  banks positions unlike the econometrician

22

• Methodology
• In-Sample Augmented GARCH
• Out-of-Sample Regression

23
(No Transcript)
24

• Conclusion (Part I)
• We use public information about VaR disclosed by
  banks in their annual reports
• Large differences in the level of disclosure
  among US commercial banks
• Upward trend in the amount of information
  disclosed to the public
• US VaR disclosures are below average
• Large differences in the level of disclosure
  across countries
• Historical Simulation is the most popular VaR
  method

25

• Conclusion (Part II)
• Unlike the level of disclosure the quality of
  VaR shows no sign of improvement over time
• Disconnection between 1-day VaR and actual
  volatility on the next day
• HS-based VaR helps little in forecasting the
  volatility of future trading revenues
• Its incremental forecasting ability over a simple
  GARCH model is very limited
• Only exception Deutsche Bank

26
The Level and Quality of Value-at-Risk Disclosure
by Commercial Banks Christophe Pérignon HEC
Paris Daniel R. Smith Simon Fraser
University Risk Management in Financial
Institutions 23-25 April 2009